Classroom Problem Solving: Math

Problem solving is mostly associated with math skills. Problem solving skills are essential to understanding and succeeding in mathematics. During the early elementary years of school children frequently go to the teacher for answers to a math problem when they do not know a solution (Myren, 1996). Students believe that every problem only has one way to be solved and those teachers or other adults are the ones to ask for a solution (Myren, 1996). To solve this dilemma teachers often allow students to work together in groups to solve problems and facilitate learning. Teachers may use children’s math abilities as a way to organize and assemble group activities, although research has stated that higher math ability students may discourage lower ability students from participating in group problem solving by controlling all operations of the group (as cited in Wilczenski, Bontrager, Ventrone, & Correia, 2001). Before assembling groups in a classroom, teachers must observe student behavior and take it into consideration to assure that each member of the group will feel confident in his/her participation (Wilczenski et al., 2001). Other research suggests that the level of student ability, group placement, and a student’s self-awareness may collectively play a role in the metacognitive processes during mathematical problem solving (Artzt & Armour-Thomas, 1997).

Teachers hope that organizing students into cooperative learning groups will facilitate learning for all members of the group. Researchers Wilczenski, Bontrager, Ventrone, & Correia (2001) studied the way students work cooperatively in groups to solve a math problem using problem solving skills. They observed how group members worked together with problem solving and also monitored each student’s personal success (Wilczenski et al., 2001). Results showed well functioning groups were successful in problem solving. Groups that did not cooperate well together scored poorly on the observations, and they also did not perform better than the control group (control group only worked individually). These results prove that group members who successfully work together will produce good quality work (Wilczenski et al., 2001).

Researchers Artzt & Armour-Thomas (1997) observed the metacognitive abilities of math students in small groups and also interviewed students about how they perceive themselves as math students and their feelings toward working in a small group setting. Researchers chose a money problem for the students to solve based on the fact that there is no set step-by-step procedure to solve it. Teachers of the students also indicated that a money problem was one that students of varying ability levels could solve and it would take organization within the group to find a solution (Artzt & Armour-Thomas, 1997).

Researchers observed not only how students cognitively solved the particular problem together, but also how they planned and organized the information metacognitively. Following group work students were interviewed and asked multiple questions about how they felt during group work (Artzt & Armour-Thomas, 1997). Higher ability math students reported feeling anxious and not feeling confident in finding a solution to the given problem, but these same students had many positive comments to say about working together in groups. Other higher ability students reported feeling confident and excited about working on the problem, but reported negative feeling about group work. Lower ability students reported feeling confused and they wanted to find their own solutions to the problem, but they all reported positive comments about working together in groups (Artzt & Armour-Thomas, 1997).

Myren (1996) conducted a study in a kindergarten classroom during math class also investigating problem solving during group work. The purpose was to encourage students to search for solutions within themselves and other group members, rather than asking the teacher. The students were separated into groups of eight or ten students. The groups were given the same math problem to solve. In the groups students were encouraged to draw, write, and discuss multiple solutions to the given problem. After the problem was read aloud to the groups of students, the teacher walked around the room and checked for understanding. Then the teacher gave each student a piece of paper to draw or write solutions. The teacher then observed problem solving techniques posed by each student within the groups. If while groups were working a student had a question, he or she was directed back to his or her group to find an answer. After each group had reached a solution, the teacher chose students from each group to present his or her problem solving strategy (Myren 1996).

The results showed that students were challenged to use problem solving skills on their own and use other group members as ways to clarify understanding of math problems. When students presented what they learned to the class, other students seemed to better understand how to solve the math problem. Myren (1996) suggests the following strategies for problem solving in the classroom: allow children plenty of time to read and reread the problem to check for understanding, interview students to check for understanding, and keep evidence of problem solving over the course of the year to monitor improvements.